A Vine Copula-Based Global Sensitivity Analysis Method for Structures with Multidimensional Dependent Variables

Zhiwei Bai,Shufang Song,Hongkui Wei,Yingying Xiao,Sergei Kucherenko

doi:10.3390/math9192489

Zhiwei Bai, Shufang Song + Show 3 more

Open Access

https://doi.org/10.3390/math9192489

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Abstract

For multidimensional dependent cases with incomplete probability information of random variables, global sensitivity analysis (GSA) theory is not yet mature. The joint probability density function (PDF) of multidimensional variables is usually unknown, meaning that the samples of multivariate variables cannot be easily obtained. Vine copula can decompose the joint PDF of multidimensional variables into the continuous product of marginal PDF and several bivariate copula functions. Based on Vine copula, multidimensional dependent problems can be transformed into two-dimensional dependent problems. A novel Vine copula-based approach for analyzing variance-based sensitivity measures is proposed, which can estimate the main and total sensitivity indices of dependent input variables. Five considered test cases and engineering examples show that the proposed methods are accurate and applicable.

Highlights

Variance-based global sensitivity analysis (GSA) is very commonly used in the area of structural safety [1,2,3]
VC1 generates dependent unconditional and conditional samples according to copula instead of the real joint cumulative distribution functions (CDF), while VC2 solves the indices respectively by decomposing the joint probability density function (PDF) into independent and dependent parts
The approaches provide a new method for variance-based GSA of multidimensional cases with different correlations

Summary

Introduction

Variance-based global sensitivity analysis (GSA) is very commonly used in the area of structural safety [1,2,3]. Kucherenko et al [10] applied a Gaussian copula method to variance-based global sensitivity analysis, and introduced a more general approach. On this basis, Song et al [11] proposed using an adaptive copula method to solve Sobol’ indices, which can describe different types of correlations. The flood peak value, total amount and duration are complexly correlated [18] For such problems, the above multivariate copula models are subject to errors [19], and the correlations should be measured by different copula functions. We introduce Vine copula [20,21,22] to the variance-based global sensitivity analysis of complex multidimensional correlation problems.

Vine Copula

Variance-Based GSA Based on Vine Copula

Test Cases

A18 A19 A20 A21 A14 A15 A16 A17

Findings

Conclusions